Stochastic Modeling of BeiDou Double-Difference Observation and Impact Analysis

Double-difference integer ambiguity resolution (IAR) is playing the vital part in the high precision GNSS positioning and navigation. The IAR success rate depends on three factors: the functional model, the stochastic model and the chosen method of the integer ambiguity estimation. Stochastic model plays an important role in parameter estimation of global navigation satellite system (GNSS). Only a correct stochastic model can be used to obtain the reliable integer ambiguity, the accurate positioning and the reliable baseline precisions. In this paper, a stochastic model with significantly sophisticated structure is designed, and the MINQUE method is utilized to estimate the cross correlations between different types of observations at arbitrary frequency and the time correlations for phase and code observations per frequency. In assessing the stochastic model, the short-length baseline and zero-length baseline with sampling frequency of 1 s are processed to analyze the impact of the realistic stochastic model considering the cross and time correlations on the IAR success rate and positioning. The results confirm that compared with the empirical stochastic model ignoring the cross and time correlations, the more realistic stochastic model can significantly improve the IAR theoretical and practical success rate, especially for single-frequency data, the practical success rate increases by 5%. The baseline precision that ignores cross and time correlation has a large difference from the theoretical ones. Namely, the baseline precision ignoring physical correlations is too optimistic and unrealistic. On the contrary, the baseline precision that considers physical correlation match the theoretical ones more well.